- #1

hopkid

- 9

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## Homework Statement

a) For the mechanism shown in figure 1 determine for the angle (45°):

i) the velocity (VBO) of the piston relative to the fixed point (O).

ii) the angular velocity of AB about point A.

iii) the acceleration of point B relative to A.

*Note: Link AB is horizontal when angle = 45°.

b) Determine the value of the angle (measured from vertical) when:

i) the velocity of point b = 0.

ii) the angular velocity of link AB a maximum.

c) what is the maximum angular velocity of link AB?

## Homework Equations

v=lw (a)r = v^2/l

## The Attempt at a Solution

l of AO = 50mm = 0.05m

l of AB = 200mm = 0.2m

w of AO = 300 x 2pi/60 = 31.42 rads^-1

ai) V of AO = l of AO x w of AO.

V of A0 = 0.05 x 31.42

V of AO = 1.57ms^-1

*Use this value to draw a velocity diagram (attached).

To confirm using trig,

Sin(45°) = V of BO/1.57

V of BO = 1.57 x Sin(45°)

V of BO = 1.11ms^-1

aii) v=lw therefore w=v/l

w of AB = v of AB/l of AB

w of AB = 1.11/0.2

w of AB = 5.55 rads^-1

aiii) (a of BA)r = v of BA^2/l of BA

(a of BA)r = 1.11^2/0.2

(a of BA)r = 6.16ms^-2

*Tangential velocity is calculated in the acceleration diagram (attached).

Radial acceleration of AO calculated below to use in the diagram.

(a of AO)r = v of AO^2/l of AO

(a of AO)r = 1.57^2/0.05

(a of AO)r = 49.3ms^-2

So, as per the diagram, (a of BA)t = 34.5ms^-2.

This is the part where I am starting to struggle, I have had conformation back from my tutor that the first 3 parts to the question look good but I am struggling with parts b & c.

If someone could help push me in the right direction then it would be very much appreciated. I am after guidance, not answers, I want to learn.